[tex](x+2)^2-x-2=x^2+4+4x-x-2=x^2-3x+2 \\
x^2-3x+2= \\
x^2-x-2x+2=x(x-1)-2(x-1)=(x-1)(x-2) \\ \\
(x+8)^2-x-8=x^2+64+16x-x-8=x^2+15x+56 \\
x^2+15x-56= \\
x^2+7x+8x-56=x(x+7)+8(x+7)=(x+7)(x+8) \\ \\
(x+1)^2+3x+3=x^2+1+2x+3x+3=x^2+5x+4 \\
x^2+5x+4= \\
x^2+x+4x+4=x(x+1)+4(x+1)=(x+1)(x+4) \\ \\
2x^3(x^3+1)-x^3(x^3+1)+x^3+1= \\
2x^6+2x^3-x^6-x^3+x^3+1=x^6+2x^3+1 \\
x^6+2x^3+1=(x^3)^2+2*x^3*1+1^2=(x^3+1)^2 \\ \\
[/tex]